Stable binary relations on universal algebras

With every universal algebra there is associated the ordered involutory semigroup of all its correspondences (stable binary relations). Two universal algebras are said to be $R$-isomorphic if their semigroups of correspondences are isomorphic. A subclass $K$ of the class $C$ of universal algebras is $R$-characterizable in $C$ if it is closed with respect to $R$-isomorphisms. In this article we single out a number of $R$-characterizable classes of universal algebras. It is shown that the complete preimage of an $R$-characterizable class is $R$-characterizable. The results obtained are applied to classes of semigroups and semiheaps.
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